Introduce simple_eval() for lazy evaluations

This patch implements the pure materialistic evaluation called simple_eval()
to gain a speed-up during Stockfish search.

We use the so-called lazy evaluation trick: replace the accurate but slow
NNUE network evaluation by the super-fast simple_eval() if the position
seems to be already won (high material advantage). To guard against some
of the most obvious blunders introduced by this idea, this patch uses the
following features which will raise the lazy evaluation threshold in some
situations:

- avoid lazy evals on shuffling branches in the search tree
- avoid lazy evals if the position at root already has a material imbalance
- avoid lazy evals if the search value at root is already winning/losing.

Moreover, we add a small random noise to the simple_eval() term. This idea
(stochastic mobility in the minimax tree) was worth about 200 Elo in the pure
simple_eval() player on Lichess.

Overall, the current implementation in this patch evaluates about 2% of the
leaves in the search tree lazily.

--------------------------------------------

STC:
LLR: 2.94 (-2.94,2.94) <0.00,2.00>
Total: 60352 W: 15585 L: 15234 D: 29533
Ptnml(0-2): 216, 6906, 15578, 7263, 213
https://tests.stockfishchess.org/tests/view/64f1d9bcbd9967ffae366209

LTC:
LLR: 2.94 (-2.94,2.94) <0.50,2.50>
Total: 35106 W: 8990 L: 8678 D: 17438
Ptnml(0-2): 14, 3668, 9887, 3960, 24
https://tests.stockfishchess.org/tests/view/64f25204f5b0c54e3f04c0e7

verification run at VLTC:
LLR: 2.94 (-2.94,2.94) <0.50,2.50>
Total: 74362 W: 19088 L: 18716 D: 36558
Ptnml(0-2): 6, 7226, 22348, 7592, 9
https://tests.stockfishchess.org/tests/view/64f2ecdbf5b0c54e3f04d3ae

All three tests above were run with adjudication off, we also verified that
there was no regression on matetracker (thanks Disservin!).

----------------------------------------------

closes #4771

Bench: 1393714

src/evaluate.cpp

@@ -136,35 +136,54 @@ namespace Eval {
   }
 }
 
-/// evaluate() is the evaluator for the outer world. It returns a static
-/// evaluation of the position from the point of view of the side to move.
 
-Value Eval::evaluate(const Position& pos) {
-
-  assert(!pos.checkers());
-
-  Value v;
+/// simple_eval() returns a static, purely materialistic evaluation of the position
+/// from the point of view of the given color. It can be divided by PawnValue to get
+/// an approximation of the material advantage on the board in terms of pawns.
 
-  int nnueComplexity;
-  int npm = pos.non_pawn_material() / 64;
+Value Eval::simple_eval(const Position& pos, Color c) {
+   return  PawnValue * (pos.count<PAWN>(c)       - pos.count<PAWN>(~c))
+           +           (pos.non_pawn_material(c) - pos.non_pawn_material(~c));
+}
 
-  Color stm = pos.side_to_move();
-  Value optimism = pos.this_thread()->optimism[stm];
 
-  Value nnue = NNUE::evaluate(pos, true, &nnueComplexity);
+/// evaluate() is the evaluator for the outer world. It returns a static evaluation
+/// of the position from the point of view of the side to move.
 
-  int material =  pos.non_pawn_material(stm) - pos.non_pawn_material(~stm)
-                + 126 * (pos.count<PAWN>(stm) - pos.count<PAWN>(~stm));
+Value Eval::evaluate(const Position& pos) {
 
-  // Blend optimism and eval with nnue complexity and material imbalance
-  optimism += optimism * (nnueComplexity + abs(material - nnue)) / 512;
-  nnue     -= nnue     * (nnueComplexity + abs(material - nnue)) / 32768;
+  assert(!pos.checkers());
 
-  v = (  nnue     * (915 + npm + 9 * pos.count<PAWN>())
-       + optimism * (154 + npm +     pos.count<PAWN>())) / 1024;
+  Value v;
+  Color stm      = pos.side_to_move();
+  int shuffling  = pos.rule50_count();
+  int simpleEval = simple_eval(pos, stm) + (int(pos.key() & 7) - 3);
+
+  bool lazy = abs(simpleEval) >=   RookValue + KnightValue
+                                 + 16 * shuffling * shuffling
+                                 + abs(pos.this_thread()->bestValue)
+                                 + abs(pos.this_thread()->rootSimpleEval);
+
+  if (lazy)
+      v = Value(simpleEval);
+  else
+  {
+      int nnueComplexity;
+      Value nnue = NNUE::evaluate(pos, true, &nnueComplexity);
+
+      Value optimism = pos.this_thread()->optimism[stm];
+
+      // Blend optimism and eval with nnue complexity and material imbalance
+      optimism += optimism * (nnueComplexity + abs(simpleEval - nnue)) / 512;
+      nnue     -= nnue     * (nnueComplexity + abs(simpleEval - nnue)) / 32768;
+
+      int npm = pos.non_pawn_material() / 64;
+      v = (  nnue     * (915 + npm + 9 * pos.count<PAWN>())
+           + optimism * (154 + npm +     pos.count<PAWN>())) / 1024;
+  }
 
   // Damp down the evaluation linearly when shuffling
-  v = v * (200 - pos.rule50_count()) / 214;
+  v = v * (200 - shuffling) / 214;
 
   // Guarantee evaluation does not hit the tablebase range
   v = std::clamp(v, VALUE_TB_LOSS_IN_MAX_PLY + 1, VALUE_TB_WIN_IN_MAX_PLY - 1);
@@ -184,6 +203,7 @@ std::string Eval::trace(Position& pos) {
 
   // Reset any global variable used in eval
   pos.this_thread()->bestValue       = VALUE_ZERO;
+  pos.this_thread()->rootSimpleEval  = VALUE_ZERO;
   pos.this_thread()->optimism[WHITE] = VALUE_ZERO;
   pos.this_thread()->optimism[BLACK] = VALUE_ZERO;
 

src/evaluate.h

@@ -21,6 +21,8 @@
 
 #include <string>
 
+#include "types.h"
+
 namespace Stockfish {
 
 class Position;
@@ -29,6 +31,8 @@ enum Value : int;
 namespace Eval {
 
   std::string trace(Position& pos);
+
+  Value simple_eval(const Position& pos, Color c);
   Value evaluate(const Position& pos);
 
   extern std::string currentEvalFileName;

src/thread.cpp

@@ -27,6 +27,7 @@
 #include <memory>
 #include <utility>
 
+#include "evaluate.h"
 #include "misc.h"
 #include "movegen.h"
 #include "search.h"
@@ -212,6 +213,7 @@ void ThreadPool::start_thinking(Position& pos, StateListPtr& states,
       th->rootMoves = rootMoves;
       th->rootPos.set(pos.fen(), pos.is_chess960(), &th->rootState, th);
       th->rootState = setupStates->back();
+      th->rootSimpleEval = Eval::simple_eval(pos, pos.side_to_move());
   }
 
   main()->start_searching();

src/thread.h

@@ -67,6 +67,7 @@ class Thread {
   Search::RootMoves rootMoves;
   Depth rootDepth, completedDepth;
   Value rootDelta;
+  Value rootSimpleEval;
   CounterMoveHistory counterMoves;
   ButterflyHistory mainHistory;
   CapturePieceToHistory captureHistory;